Are OBJ files exported from Blender different?
A problem blender has in comparison with most other software is its axis differences. Blender uses +Z up, +Y forward, +X right, whereas most others are different. Maya, for example, uses +Z backward, +Y up, +X right; C4D uses +Z forward, +Y up, +X right... It's a mess.





In the export settings, you can set which axes are up and forward. By default, they follow the convention that allows them to import into Maya properly, ie -Z forward, +Y up. 

After Effects may be different. I believe +Z is coming towards you and +Y is up. The point here is that you might need to experiment with the axis export settings to get the proper orientation of your object in AE. 

Key point to remember is that from the front camera view, forward is going away from you, right is right, up is up. A quick and easy way to test these settings is to just use Suzanne as a test model. She's light and easily recognizable, much more so than a cube. Once you get her to export right, just use those settings for your other objects.